Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Assignment Testers: Towards a Combinatorial Proof of the PCP-Theorem
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Simple PCPs with poly-log rate and query complexity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
The PCP theorem by gap amplification
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding
SIAM Journal on Computing
Sparse Random Linear Codes are Locally Decodable and Testable
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Tensor Products of Weakly Smooth Codes Are Robust
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
The tensor product of two codes is not necessarily robustly testable
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Robust local testability of tensor products of LDPC codes
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Low rate is insufficient for local testability
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Guest column: testing linear properties: some general theme
ACM SIGACT News
On the rectangle method in proofs of robustness of tensor products
Information Processing Letters
The tensor product of two good codes is not necessarily robustly testable
Information Processing Letters
A new family of locally correctable codes based on degree-lifted algebraic geometry codes
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We continue the study of the local testability of error correcting codes constructed by taking the two-wise tensor product of a "base-code" with itself. We show that if the base-code is any locally testable code (LTC) or any expander code, then the code obtained by taking the repeated two-wise tensor product of the base-code with itself is locally testable. This extends the results of Dinur et al. in [11] in two ways. First, we answer a question posed in that paper by expanding the class of allowed base-codes to include all locally testable code, and not just so-called uniform LTCs whose associated tester queries all codeword entries with equal probability. Second, we show that repeating the two-wise tensor operation a constant number of times still results in a locally testable code, improving upon previous results which only worked when the tensor product was applied once . To obtain our results we define a new tester for the tensor product of LTCs. Our tester uses the distribution of the tester associated with the base-code to sample rows and columns of the product code. This construction differs from previously studied testers for tensor product codes which sampled rows and columns uniformly .